Department of Mathematics
A Dilation Theorem For Invariant Weakly Positive Semidefinite Kernels Valued In Admissible Spaces
Abstract: An ordered *-space Z is a complex vector space with a conjugate linear
involution *, and a strict cone Z+ consisting of self-adjoint elements. An
admissible space in the sense of Loynes is an ordered *-space with a complete
locally convex topology, compatible with the
partial ordering of its cone. We consider weakly positive semidefinite
kernels that are invariant under a left action of a *-semigroup and valued in
an admissible space. Under a suitable boundedness condition we obtain VH
(Vector Hilbert) space linearisations and equivalently, reproducing kernel
VH-spaces and *-representations of the *-semigroup on them. As applications of
main theorem, we obtain various known dilation theorems with a suitable choice of a kernel and an admissible space. This is a joint work with A. Gheondea.
Date: Thursday, November 24, 2016
Place: Mathematics Seminar, SA-141
Tea and cookies will be served before the seminar.